Recent progress in generalized moonshine
Tuesday, 8.4.14, 14:15-15:15, Raum 404, Eckerstr. 1
Monstrous moonshine started in the 1970s, when McKay and some others found apparent numerical coincidences relating modular functions on the complex upper half plane and linear representations of the monster simple group. We now know that the numerical relationships that were initially seen can be explained by the existence of the monster vertex algebra. Later computations by Queen and Norton suggested that certain subgroups of the monster also yielded modular functions from their representation theory, and this was codified by Norton in his generalized moonshine conjecture. I will describe this conjecture, a mathematical interpretation arising from orbifold conformal field theory, and some recent progress.\n
Programmdiskussion
Monday, 28.4.14, 16:15-17:15, Raum 404, Eckerstr. 1
Preview
Tuesday, 29.4.14, 16:15-17:15, Raum 404, Eckerstr. 1
Scharf 2-transitive Gruppen
Wednesday, 30.4.14, 16:30-17:30, Raum 404, Eckerstr. 1
Test
Thursday, 1.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
An isomorphism of > motivic Galois groups
Friday, 2.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Strong convergence with rates for discretizations of SPDEs with non-Lipschitz drift
Tuesday, 6.5.14, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
I discuss the convergence analysis for space-time discretizations of three nonlinear SPDEs: the stochastic Navier-Stokes equation, the stochastic Allen-Cahn equation, and the stochastic mean curvature flow of planar curves of graphs.\n\nDepending on the drift operator, optimal rates with respect to strong convergence are valid for errors on large subsets, or on the whole sample set.
The area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain
Tuesday, 6.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
tba
Wednesday, 7.5.14, 16:00-17:00, Raum 404, Eckerstr. 1
Thursday, 8.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Non-Commutative Polynomial Optimization
Friday, 9.5.14, 14:00-15:00, Hörsaal I, Physik Hochhaus, Hermann-Herder Straße 3
In this talk, I consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed; and the associated polynomial inequalities, as semidefinite positivity constraints. To solve these problems, I introduce a complete hierarchy of semidefinite programming relaxations. This hierarchy, that can be understood as the non-commutative analogue of the Lasserre-Parrilo method for polynomial minimization, gives the user the power to make rigorous claims about the possible expectation values of infinite dimensional operators satisfying a number of polynomial identities. I will review several applications that noncommutative polynomial optimization has found in physics and quantum information theory since the conception of our hierarchy, as well as some interesting extensions of the original method. Finally, I will list some of the current challenges of this young field.
String-Topology
Monday, 12.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Local solutions to a free boundary problem for the Willmore functional
Tuesday, 13.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
The generalized Lipman-Zariski problem
Thursday, 15.5.14, 10:15-11:15, Raum 403, Eckerstr. 1
We study a generalized version of the Lipman-Zariski conjecture: let (x in X) be an n-dimensional singularity such that for some integer 1 <= p <= n - 1, the sheaf Omega_X^[p] of reflexive differential p-forms is free. Does this imply that (x in X) is smooth? We give an example showing that the answer is no even for p = 2 and X a terminal threefold. However, we prove that if p = n - 1, then there are only finitely many log canonical counterexamples in each dimension, and all of these are isolated and terminal.\nOn the other hand, if (x in X) is a hypersurface singularity with singular locus of codimension at least three, we give an affirmative answer to the above question for any 1 <= p <= n - 1.
Compatible discrete operator schemes for elliptic problems on polyhedral meshes
Thursday, 15.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Compatible discrete operator schemes aim at preserving basic\nproperties of the continuous problem at the discrete level. We analyze a\nclass of such schemes for a model elliptic problem. The cornerstone in\nthe design of the scheme is the discrete Hodge operator linking discrete\ngradient and fluxes. We present the two abstract properties to be\nsatisfied by this operator to achieve convergence. Then, we focus on the\ndesign of this operator using the concept of local gradient\nreconstruction. We highlight connections to various schemes developed in the literature.\n Finally, we present numerical examples.
Symmetries of the Hesse pencil with applications
Friday, 16.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
The Hesse normal form t(x^3+y^3+z^3)+uxyz=0 allows an efficient implementation of the arithmetic on an elliptic curve and immediately exhibits the 9 inflection points in characteristic different from 3.\nFurthermore Artebani and Dolgachev have shown that the group of projective transformations leaving the Hesse pencil invariant can be realized as a group of automorphisms on a singular K3 surface (i.e. one with Picard number 20 in characteristic 0). I intend to demonstrate the\nconstruction of one such surface.
How superadditive can a risk measure be?
Friday, 16.5.14, 11:30-12:30, Raum 404, Eckerstr. 1
Der Satz von Poincare-Hopf für Laminationen
Monday, 19.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Analysis on QAC manifolds
Tuesday, 20.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk I will present a program for doing analysis on QAC spaces. These are geometries that generalize the AC (asymptotically conical) manifolds.
Tuesday, 20.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
test
Free amalgamation and automorphism groups
Wednesday, 21.5.14, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 22.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Minkowski decompositions
Friday, 23.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Developing Prediction Models and Visualization Tools for Predictive Toxicology
Friday, 23.5.14, 11:30-12:30, Raum 404, Eckerstr. 1
Smoothing theory on homology spheres and its application on Algebraic K-theory
Monday, 26.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Willmore Fläche I
Tuesday, 27.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Thursday, 29.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Tilting Theory via Stable Homotopy Theory
Friday, 30.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Tilting theory is a derived version of Morita theory.\nIn the context of quivers Q and Q' and a field k, this ammounts to looking for conditions which guarantee that the derived categories of the path algebras D(kQ) and D(kQ') are equivalent as triangulated categories.\n\nIn this project (which is j/w Jan Stovicek) we take a different approach to tilting theory and show that some aspects of it are formal consequences of stability. Slightly more precisely, we show that certain tilting\nequivalences can be lifted to the context of arbitrary stable derivators. Plugging in specific examples this tells us that refined versions of these tilting results are also valid over arbitrary ground rings, for quasi-coherent modules on a scheme, in the differential-graded context, and also in the spectral context.
The Renormalisation Group via Statistical Inference
Friday, 30.5.14, 14:00-15:00, Hörsaal I, Physik Hochhaus, Hermann-Herder Straße 3
In physics one attempts to infer the rules governing a system given only\nthe results of imperfect measurements. Hence, microscopic theories may\nbe effectively indistinguishable experimentally. We develop an\noperationally motivated procedure to identify the corresponding\nequivalence classes of theories. Here it is argued that the\nrenormalisation group arises from the inherent ambiguities in\nconstructing the classes: one encounters flow parameters as, e.g., a\nregulator, a scale, or a measure of precision, which specify\nrepresentatives of the equivalence classes. This provides a unifying framework and identifies the role played by information in renormalisation. Our methods also provide a way to extend\nrenormalisation techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the distinctions between various type of RG.
Periodic orbits in cotangent bundles of non-compact manifolds
Monday, 2.6.14, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk I will discuss some existence results for periodic orbits on fixed\nenergy levels of mechanical Hamiltonian systems. In particular, these\nenergy hypersurfaces are allowed to be non-compact.\nI will focus on the analytical and geometrical problems posed by the lack of \ncompactness and discuss advantages and limitations of our method of proof \n("linking"). This is joint work with T. Rot, J.B. van den Berg and R. Vandervorst.
Willmore surfaces (after T Riviere, S Alexakis, R Mazzeo)
Tuesday, 3.6.14, 16:15-17:15, Raum 404, Eckerstr. 1
Strict non-forking in resilient theories
Wednesday, 4.6.14, 16:30-17:30, Raum 404, Eckerstr. 1
Symmetries of N=4 non-linear sigma models
Thursday, 5.6.14, 12:00-13:00, Raum 404, Eckerstr. 1
Thursday, 5.6.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Fibered Derivators, (Co)homological Descent and the Six-Functor Formalism
Friday, 6.6.14, 14:00-15:00, Hörsaal II, Albertstr. 23b
Fibered Derivators, (Co)homological Descent and the Six-Functor Formalism
Friday, 6.6.14, 14:00-15:00, Hörsaal II, Albertstr. 23b
Symmetric Powers and Multivalued Maps over an Arbitrary Base
Friday, 6.6.14, 15:00-16:00, Hörsaal II, Albertstr. 23b
Motivic Cell Structures of Homogeneous Spaces
Friday, 6.6.14, 16:15-17:15, Hörsaal II, Albertstr. 23b
Non-unitary trace formulae
Friday, 6.6.14, 17:15-18:15, Hörsaal II, Albertstr. 23b
Sonderkolloquium Angewandte Mathematik
Thursday, 12.6.14, 11:00-12:00, Raum 404, Eckerstr. 1
Thursday, 12.6.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Sonderkolloquium Angewandte Mathematik
Friday, 13.6.14, 08:45-09:45, Raum 404, Eckerstr. 1
Algebraic cycles of abelian schemes
Friday, 13.6.14, 10:15-11:15, Raum 125, Eckerstr. 1
Let X be a variety and consider the cycle class map, which maps the Chow groups of X to the cohomology groups of X. Hodge or Tate conjectures predict what should be the image of such a map, and Bloch-Beilinson-Murre conjecture predicts some structures on the kernel. We will investigate these conjectures when X is an abelian scheme, and especially when it is the universal abelian scheme over a PEL Shimura variety
Supersimplicity and the Fitting subgroup
Wednesday, 18.6.14, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 19.6.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Filtering the Grothendieck spectrum of varieties
Friday, 20.6.14, 10:15-11:15, Raum 404, Eckerstr. 1
Maaß-Formen
Monday, 23.6.14, 16:15-17:15, Raum 404, Eckerstr. 1
Willmore Fläche II
Tuesday, 24.6.14, 16:15-17:15, Raum 404, Eckerstr. 1
dp-minimality, strong dependence and dp-rank in Ordered Abelian Groups
Wednesday, 25.6.14, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 26.6.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Applications of Morse theory to cuplength estimates in symplectic geometry
Monday, 30.6.14, 16:15-17:15, Raum 404, Eckerstr. 1
There are many estimates in symplectic geometry which provide a lower bound for the number of, e.g., periodic orbits of Hamiltonian systems or Hamiltonian chords of Lagrangian submanifolds.\nIn this talk, I will describe various Floer theories related to these estimates and sketch a Morse theoretic argument which can be applied to the Floer settings to give a unifoed proof of these estimates. Moreover, this argument is also applicable in other cases, where the corresponding cuplength estimates was not known before.
Uniformity functions in descriptive set theory
Tuesday, 1.7.14, 14:00-15:00, SR119, Eckerstr. 1
Lagrangian submanifolds and examples
Tuesday, 1.7.14, 16:15-17:15, Raum 404, Eckerstr. 1
Decomposition, dimension, and degrees
Wednesday, 2.7.14, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 3.7.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
The monodromy group of stratified bundles
Friday, 4.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
On a variety over a field of positive characteristic a stratified bundle is exactly what a flat connection is on a smooth manifold. Moreover, via the theory of Tannakian categories one can endow a stratified bundle with a monodromy group, in parallel with the complex case. We will see how this group varies in smooth families, proving a strong form of the positive equicharacteristic p-curvature theorem proposed by Esnault and Langer.
Value-at-Risk aggregation under uncertainty
Friday, 4.7.14, 11:30-12:30, Raum 404, Eckerstr. 1
Rigidity results, inverse curvature flows and Alexandrov-Fenchel inequalities in the sphere
Monday, 7.7.14, 16:00-17:00, Hörsaal II, Albertstr. 23b
Aubry-Mather theory on manifolds
Monday, 7.7.14, 16:15-17:15, Raum 404, Eckerstr. 1
Finite time behavior and convergence of the Calabi flow
Monday, 7.7.14, 17:30-18:30, Hörsaal II, Albertstr. 23b
In his seminal work, E. Calabi introduced the notion called extremal Kähler metrics in a fixed cohomology class of Kähler metrics. The extremal Kähler metrics are the critical points of the Calabi energy which is the \(L^2\)-norm of the scalar curvature. The Kähler-Einstein metrics and which are more general, the constant scalar curvature Kähler metrics are both extremal Kähler metrics. In the same paper, Calabi also introduced a decreasing flow of the Calabi energy, which is now well-known as the Calabi flow. The Calabi flow is expected to be an effective tool to find the extremal Kähler metrics. Unfortunately, it is believed to be difficult to understand because of its fourth order and fully nonlinearity. However, in this talk we would like to describe its finite time singularities and asymptotic behavior.\n
On sizes of trees
Wednesday, 9.7.14, 16:30-17:30, Raum 404, Eckerstr. 1
All automorphisms of the Calkin algebra are inner
Thursday, 10.7.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
The generalized Lipman-Zariski problem
Friday, 11.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
The real and the holomorphic Chern-Simons functional
Monday, 14.7.14, 16:15-17:15, Raum 404, Eckerstr. 1
Definably amenable NIP groups
Wednesday, 16.7.14, 16:30-17:30, Raum 404, Eckerstr. 1
Numerical Optimization for Control and Estimation
Thursday, 17.7.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
The order of the reductions of points on algebraic groups
Friday, 18.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
Intersection Cohomology
Friday, 18.7.14, 15:00-16:00, Hörsaal II, Albertstr. 23b
This will be an overview of intersection cohomology and\nits various incarnations in simplicial cohomology,\nsheaf cohomology and D-module theory. I try to answer a demand of some members of the Graduiertenkolleg. The talk may well turn into a questions and answers session after a while.
Rigidity properties of metric measure spaces with generalized lower Ricci curvature bounds
Monday, 21.7.14, 13:00-14:00, Raum 127, Eckerstr. 1
In this talk I will present a maximal diameter theorem for metric measure spaces that satisfy a Riemannian curvature-dimension condition. That is, if there is equality in the Bonnet-Myers estimate, the space is a spherical suspension.\nTopological rigidity results for metric measure spaces that satisfy a measure contraction property in general fail. We present a counterexample. This is a joint work with T. Rajala.
Lagrangian mean curvature flow
Monday, 21.7.14, 14:30-15:30, Raum 127, Eckerstr. 1
Mean curvature flow of pinched submanifolds in positively curved symmetric spaces
Monday, 21.7.14, 16:00-17:00, Raum 127, Eckerstr. 1
The Mathieu group \(M_{24}\)
Monday, 21.7.14, 16:15-17:15, Raum 404, Eckerstr. 1
Tuesday, 22.7.14, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Discontinuous Galerkin Methods for Isogeometric Analysis for Elliptic and Allen-Cahn Equations on Surfaces
Tuesday, 22.7.14, 15:30-16:30, Raum 226, Hermann-Herder-Str. 10
Somre results on the coupling between the Ricci flow and the mean curvature flow
Tuesday, 22.7.14, 16:15-17:15, Raum 404, Eckerstr. 1
Some results on the coupling between the Ricci flow and the mean curvature flow
Tuesday, 22.7.14, 16:15-17:15, Raum 404, Eckerstr. 1
Schöne Gruppen
Wednesday, 23.7.14, 16:30-17:30, Raum 404, Eckerstr. 1
Sheaf-theoretic analogues of Mathai-Quillen forms
Thursday, 24.7.14, 12:00-13:00, Raum 404, Eckerstr. 1
In this talk we review certain generalizations of Mathai-Quillen forms.\nOrdinary Mathai-Quillen forms are representations of Thom classes, and\nplay an important role in topological field theories. We shall\ndiscuss analogues appearing in more recent pseudo-topological\nfield theories, involving representations of certain sheaf cohomology\nclasses which reduce to ordinary Mathai-Quillen forms in special cases.\nWe discuss some basic properties and make a few conjectures.
Thursday, 24.7.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Ein Theorem von Borcherds im Fall klassischer Modulformen
Friday, 25.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
An overview of mirror symmetry
Friday, 25.7.14, 14:00-15:00, Hörsaal II, Albertstr. 23b
In this talk I will give a gentle introduction to and\noverview of "mirror symmetry", a duality\nin two-dimensional quantum field theories\nin which theories with different interpretations are secretly equivalent.\nHistorically, mirror symmetry was a launching point for Gromov-Witten theory.\nWe review mirror symmetry and its role, and then outline modern extensions\nsuch as homological mirror symmetry and especially (0,2) mirror symmetry.
TBA
Monday, 28.7.14, 16:15-17:15, Raum 404, Eckerstr. 1
Bewertete Körper mit Automorphismus und NTP2
Wednesday, 30.7.14, 16:30-17:30, Raum 404, Eckerstr. 1
Vorstellungsvortrag: Baumwertige Fleming-Viot Prozesse mit Mutation und Selektion
Thursday, 31.7.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
In der mathematischen Populationsgenetik spielen Fleming-Viot\nProzesse eine sehr wichtige Rolle. Diese sind Verallgemeinerungen der Wright-Fisher\nProzesse und beschreiben die Evolution von Allelfrequenzen in einer Population.\nFleming-Viot Prozesse gehören zur Klasse wahrscheinlichkeitsmaßwertiger Markov-\nprozesse und werden oft mit Hilfe der dualen Koaleszenten studiert, die die\ngenealogische Struktur der Population beschreiben.\nBaumwertige Prozesse modellieren die Evolution der Population gemeinsam mit der\nzugehörigen genealogischen Struktur. Wir beschreiben die Konstruktion dieser\nProzesse und diskutieren einige ihrer Eigenschaften.\nDer Vortrag basiert auf gemeinsamen Arbeiten mit Andreas Greven und\nPeter Pfaffelhuber.\n
Reilly type formula and its application to Heintze-Karcher type inequality
Tuesday, 5.8.14, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk, a Heintze-Karcher type inequality will be\nshowed for compact manifolds with boundary and sectional curvature bounded below by -1. Our proof was based on a new Reilly type formula and solvability of a Dirichlet boundary value problem. The case of hyperbolic spaces was previously proved by Simon Brendle via a totally different approach. This is joint work with Guohuan Qiu.\n
Reilly type formula and its application to Heintze-Karcher type inequality
Tuesday, 5.8.14, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk, a Heintze-Karcher type inequality will be showed for compact manifolds with boundary and sectional curvature bounded below by -1. Our proof was based on a new Reilly type formula and solvability of a Dirichlet boundary value problem. The case of hyperbolic spaces was previously proved by Simon Brendle via a totally different approach. This is joint work with Guohuan Qiu.
Some Interesting Aspects of a Simple Model of "Non-commutative Quantum Mechanics"
Monday, 25.8.14, 16:15-17:15, Raum 404, Eckerstr. 1
Recently there has been much interest in studying a two-dimensional model of quantum mechanics, where the two components of position, and possibly also momentum, are made non-commutative. The understanding here is that such a model might mimic a non-standard structure of space at very short distances. In this talk we discuss some group theoretical aspects of such a model and some generalized complex Hermite polynomials associated with it. \n\n
Autormorphisms of Curves
Wednesday, 10.9.14, 14:00-15:00, Raum 404, Eckerstr. 1